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  • Kurujyibwami, Celestin (författare)
  • Admissible transformations and the group classification of Schrödinger equations
  • 2017
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
  • Nyagahakwa, Venuste, et al. (författare)
  • Sets with the Baire property in topologies formed from a given topology and ideals of sets
  • 2017
  • Ingår i: Questions and answers in General Topology. - Osaka : Symposium of General Topology / Iso Shinpojumu. - 0918-4732. ; 35:1, s. 59-76
  • Tidskriftsartikel (refereegranskat)abstract
    • Let X be a set, τ1, τ2 topologies on X and Bp(X, τi) the family of all subsets of X possessing the Baire property in (X, τi), i = 1, 2. In this paper we study conditions on τ1 and τ2 that imply a relationship (for example, inclusion or equality) between the families Bp(X, τ1) and Bp(X, τ2). We are mostly interested in the case where the topology τ2 is formed with the help of a local function defined by the topology τ1 and an ideal of sets I on X. We also consider several applications of the local function defined by the usual topology on the reals and the ideal of all meager sets there, for proving some known facts.
  • Emamizadeh, B., et al. (författare)
  • Optimal harvesting strategy based on rearrangements of functions
  • 2018
  • Ingår i: Applied Mathematics and Computation. - Amsterdam : Elsevier. - 0096-3003 .- 1873-5649. ; 320, s. 677-690
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. © 2017 Elsevier Inc.
  • Dupuch, Marie, et al. (författare)
  • Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms
  • 2013
  • Ingår i: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885. - Berlin Heidelberg : Springer. - 9783642383250 - 9783642383267 ; , s. 58-67
  • Bokkapitel (refereegranskat)abstract
    • In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of the methods whichcan be exploited for this. In our study, we propose to test three methodsdedicated to the clustering of terms (hierarchical ascendant classification,Radius and maximum), to combine them with the semantic distance algorithmsand to compare them through the results they provide whenapplied to terms from the pharmacovigilance area. The comparison indicatesthat the non disjoint clustering (Radius and maximum) outperformthe disjoint clusters by 10 to up to 20 points in all the experiments.
  • Lundengård, Karl, 1987- (författare)
  • Generalized Vandermonde matrices and determinants in electromagnetic compatibility
  • 2017
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.
  • Almquist, Martin, et al. (författare)
  • Atmospheric Sound Propagation Over Large-Scale Irregular Terrain
  • 2014
  • Ingår i: Journal of Scientific Computing. - 0885-7474 .- 1573-7691. ; 61:2, s. 369-397
  • Tidskriftsartikel (refereegranskat)abstract
    • A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate finite difference approximation of a high-fidelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.
  • Eriksson, Kimmo, et al. (författare)
  • Optimal Expected Rank in a Two-Sided Secretary Problem
  • 2007
  • Ingår i: Operations Research. - 0030-364X .- 1526-5463. ; 55:5, s. 921-931
  • Tidskriftsartikel (refereegranskat)abstract
    • In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
  • Eriksson, T., et al. (författare)
  • Successive Encoding of Correlated Sources
  • 1982
  • Rapport (övrigt vetenskapligt)abstract
    • The encoding of a discrete memoryless multiple source  for reconstruction of a sequence  with  is considered. We require that the encoding should be such that  is encoded first without any consideration of  , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case  . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out.
  • Feng, Bin, et al. (författare)
  • An Improved RRT Based Path Planning with Safe Navigation
  • 2014
  • Ingår i: Proceedings from the 2013 International Symposium on Vehicle, Mechanical, and Electrical Engineering, ISVMEE 2013, Taiwan, China, 21-22 December. - 9783038350033 ; , s. 1080-1083
  • Konferensbidrag (refereegranskat)abstract
    • Path planning has been a crucial problem in robotics research. Some algorithms, such as Probabilistic Roadmaps (PRM) and Rapidly-exploring Random Trees (RRT), have been proposed to tackle this problem. However, these algorithms have their own limitations when applying in a real-world domain, such as RoboCup Small-Size League (SSL) competition. This paper raises a novel improvement to the existing RRT algorithm to make it more applicable in real-world.
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